I completed the SDI/ TDI Solo course a couple of months back. What was said above is a good summary. The diving skills were nothing new. I had to lug a pony around with me, but that is not exactly the most challenging. Otherwise there were no new skills not covered in your OW course.
I was expected to be proficient at buoyancy control, SMB deployment, navigation and general diving skills. More than anything else, I asked the TDI instructor to confirm if he thought I was ready for tech training as part of the dives.
I found the knowledge component more interesting. This was all the same information from the OW and AOW courses but in a little more detail with emphasis that you need to be able to deal with problems underwater yourself (without panic). The gas planning was interesting and gave some new insights into my SAC rate and planning around it.
Overall, I got some more confidence, confirmation that I was ready for tech (in the eyes of one instructor), a renewed focus on potential underwater problems and a card that I can use in the States when I don't have a buddy available.
Solo diving can be done safely, but carries additional risks that you should be aware of and trained to handle. It is a common practice here in NY and I have encountered solo divers on a few dive boats.
If you really only want the knowledge, spend $30 on Amazon. ("SDI Solo") THIS COVERS THE KNOWLEDGE ONLY AND IS NOT A FULL SOLO COURSE. CONSULT AN INSTRUCTOR. Spend the rest of the cost of the course on getting your car fixed. (or air fills
)
If you do choose to do the course (need 100 logged dives to start) the emphasis on self sufficiency is good.
Some observations to your post:
Diving as a 3 buddy team is not solo as you have someone to help. Similarly, you are effectively solo with an inexperienced buddy, just with the false security.
Haphazardly lagging behind two buddies to check out some stuff is not solo diving, it is poor buddy diving. Solo is a planned activity. It is more important to plan your dive fully when solo.